Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

Four friends are sitting on a tree. Each one of them is wearing a hat. They don't know which coloured hat are they wearing but they do know that two of them have green hats and two of them have orange hats.

Adam is sitting on the top branch and he can see the hats of Billy and Cyrus. Billy is sitting on a branch above Cyrus and he can see Cyrus hat. Duke is sitting at the base of the tree. Branches are covering him fully and no one can see his hat.

Now they are not allowed to look upwards. Who do you think will shout the colour of his hat first?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

If six children and two dogs were under an umbrella, how come none of them got wet?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

Can you circle exactly four of these numbers such that the total is twelve?

1 6 1
6 1 6
1 6 1
6 1 6